To determine the center of the circle given by the equation [tex]\((x - 3)^2 + (y + 3)^2 = 4\)[/tex], we need to compare it to the standard form of a circle's equation.
The standard form of the equation of a circle is:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
Here:
- [tex]\((h, k)\)[/tex] represents the center of the circle.
- [tex]\(r\)[/tex] represents the radius of the circle.
Given the equation of the circle:
[tex]\[ (x - 3)^2 + (y + 3)^2 = 4 \][/tex]
We can compare this to the standard form:
- The term [tex]\((x - 3)^2\)[/tex] indicates that [tex]\(h = 3\)[/tex].
- The term [tex]\((y + 3)^2\)[/tex] can be rewritten as [tex]\((y - (-3))^2\)[/tex], indicating that [tex]\(k = -3\)[/tex].
Therefore, the center of the circle is [tex]\((h, k) = (3, -3)\)[/tex].
So, the answer is:
B. [tex]\((3, -3)\)[/tex]
